We study the evolution of oxygen abundance radial gradients as a function of time for the Milky Way Galaxy obtained with our {\sc Mulchem} chemical evolution model. We review the recent data of abundances for different objects observed in our Galactic disc. We analyse with our models the role of the growth of the stellar disc, as well as the effect of infall rate and star formation prescriptions, or the pre-enrichment of the infall gas, on the time evolution of the oxygen abundance radial distribution. We compute the radial gradient of abundances within the {\sl disk}, and its corresponding evolution, taking into account the disk growth along time. We compare our predictions with the data compilation, showing a good agreement. Our models predict a very smooth evolution when the radial gradient is measured within the optical disc with a slight flattening of the gradient from $\sim -0.057$\,dex\,kpc$^{-1}$ at $z=4$ until values around $\sim -0.015$\,dex\,kpc$^{-1}$ at $z=1$ and basically the same gradient until the present, with small differences between models. Moreover, some models show a steepening at the last times, from $z=1$ until $z=0$ in agreement with data which give a variation of the gradient in a range from $-0.02$ to $-0.04$\,de\,kpc$^{-1}$ from $t=10$\,Gyr until now. The gradient measured as a function of the normalized radius $R/R_{\rm eff}$ is in good agreement with findings by CALIFA and MUSE, and its evolution with redshift falls within the error bars of cosmological simulations.

19 pages, 11 figures, MNRAS, in press